I'd look up Amazon or Ebay digital temperature controllers, which are basically thermostats but more designed for process control applications than room heating and cooling. Most of them have a remote sensor of some sort--a thermistor most likely for the temperature range we're talking about--and can be set to have whatever setpoint, hysteresis, etc. one may wish. Putting the sensor in the wet bay and wiring the controller in parallel with the thermostat would seem to me to work reliably and simply. The furnace would come on whenever either the room thermostat or the wet bay temperature controller called for heat, and go off only when both are satisfied.
The obvious advantage to this over a time control is that you get the heat you need, but not more or less. If the temperature drops too much, the periodic run might not be enough heat; and if it's only a little below freezing, it could be a good bit more than is necessary.
A couple of examples of these sorts of controllers (no idea if these are any better or worse than others, nor how well they'd cope with "12V" supplies that are much more or less than the nominal voltage):
Cheap and simple bare-board,
More finished looking panel mount unitFifteen minutes of running the furnace when you already have the interior at room temperature is going to make it a fair bit warmer, I suspect. Shorter and more frequent cycles would probably be better overall. That's not much more than a semi-educated guess, though.